# Effect of reflector curvature on a plane wave

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 6 |

Pages | 181 - 220 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 6.4

Redraw Figure 6.4a for a plane wave incident on the reflector, and explain the significance of the changes which this makes.

### Background

Figure 6.4a assumes a point source at the surface, whereas for an incident plane wave in Figure 6.4b the source is at infinity. The plane wave reflected by the plane reflector produces a plane wavefront (*R*), i.e., the reflected wavefront has zero curvature. For a point diffractor the virtual source is at the diffractor and the wavefront has the maximum curvature (*D*). The curvature of the wavefront from the anticlinal reflector (*A*) is intermediate between those of and and the curvature of the wavefront from the synclinal reflector (*S*) is negative (assuming the center of curvature is below the surface).

### Solution

By Huygens’s principle (problem 3.1), a diffracting point acts as a point source whenever a wave falls upon it; hence, the diffraction response to a plane wave (Figure 6.4b) is the same as that in Figure 6.4a. A plane wave incident on a plane reflector gives rise to a reflected plane wave . For a plane wave incident on an anticline or syncline of circular cross-section of radius , we can use the mirror formula, namely,

where is the focal length , and are the distances of the source and reflected image from the apex of an anticline or trough of a syncline; is positive for a syncline and is infinite for a plane wave, so . For a syncline, the reflected wave comes to a focus a distance above the trough. For an anticline, a virtual image (see problem 4.1) is at below the high point.

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Reflection and refraction laws and Fermat’s principle | Diffraction traveltime curves |

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Geometry of seismic waves | Characteristics of seismic events |

## Also in this chapter

- Characteristics of different types of events and noise
- Horizontal resolution
- Reflection and refraction laws and Fermat’s principle
- Effect of reflector curvature on a plane wave
- Diffraction traveltime curves
- Amplitude variation with offset for seafloor multiples
- Ghost amplitude and energy
- Directivity of a source plus its ghost
- Directivity of a harmonic source plus ghost
- Differential moveout between primary and multiple
- Suppressing multiples by NMO differences
- Distinguishing horizontal/vertical discontinuities
- Identification of events
- Traveltime curves for various events
- Reflections/diffractions from refractor terminations
- Refractions and refraction multiples
- Destructive and constructive interference for a wedge
- Dependence of resolvable limit on frequency
- Vertical resolution
- Causes of high-frequency losses
- Ricker wavelet relations
- Improvement of signal/noise ratio by stacking